Vertex-transitive

Vertex-transitive

Vertex-transitive refers to a property of a graph where for any pair of vertices, there exists an automorphism of the graph that maps one vertex to the other. This means that the automorphism group of the graph acts transitively on its vertices by function application.From: Diagnosability of arrangement graphs with missing edges under the MM* model [2020], Graph Theory and Interconnection Networks [2019], The Garden of Eden theorem for cellular automata on group sets [2019]

Onion-Like Inorganic Fullerenes from a Polyhedral Perspective

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Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020

Ch. Chang, A. B. C. Patzer, D. Sülzle, H. Bauer

The Catalan solids are all convex. They are face-transitive but not vertex-transitive, i.e. all faces are equivalent but the vertex environments are not. This is because the Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular, and they have constant dihedral angles. Being face-transitive, Catalan solids are isohedral i.e. there is just one kind of face.

Diagnosability of arrangement graphs with missing edges under the MM* model

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Published in International Journal of Parallel, Emergent and Distributed Systems, 2020

Shiying Wang, Xiaolei Ma

A graph is vertex-transitive if and only if for its any pair of vertices u and v, there exists an automorphism of the graph that maps u to v. A graph is edge-transitive if and only if for its any pair of edges and , there exists an automorphism of the graph that maps to .

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Onion-Like Inorganic Fullerenes from a Polyhedral Perspective

Diagnosability of arrangement graphs with missing edges under the MM* model